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Lesson Example Discussion Quiz: Class Homework

Quiz In Class

Title: Complex Numbers

Grade: 10-a Lesson: S2-L8

Explanation: Hello Students, time to practice and review. Let us take next 10-15 minutes to solve the ten problems using the Quiz Sheet. Then submit the quiz to get the score. This is a good exercise to check your understanding of the concepts.

Quiz: in Class

Problem Id	Problem	Options
1	Evaluate \$(1 + i)^3\$.	A) -2 + 5i B) -1 + 2i C) -2 + 2i D) -2 - 2i
2	Solve the equation \$ z^2 + 6z + 25 = 0\$ for z.	A) z = 1 + 4i and z = 1 − 4i B) z = −2 + 5i and z = −2 − 5i C) z = 2 + 4i and z = 2 − 4i D) z = −3 + 4i and z = −3 − 4i
3	Multiply the complex numbers (2 + 3i) and (- 1 + 2i).	A) - 4 + 3i B) - 8 + i C) - 6 + i D) - 2 + 4i
4	Divide the complex numbers: \$(5 + 7i) / (2 - 3i)\$.	A) \$ (-11/13) + (29/13)i \$ B) \$ (-21/11) + (25/11)i \$ C) \$ (21/11) + (25/11)i \$ D) \$ (1/13) + (29/13)i \$
5	Find the roots of a complex polynomial \$z^3 + 4z^2 + 5z + 2 = 0\$.	A) z = - 1, - 1, - 2 B) z = 0, - 1, 2 C) z = 1, 1, - 2 D) z = 2, - 3, 4
6	Find the sum of all complex numbers z such that \$z^3 + 2z^2 + z − 3 = 0\$.	A) - 3 B) - 2 C) - 6 D) 4
7	Perform operations with complex numbers. Let’s solve the following expression: \$(3 + 2i) + (1 − 4i) times (2 + 3i)\$.	A) 15 - 3i B) 17 - 3i C) 11 - 5i D) 7 - 3i
8	Solve a quadratic equation with complex roots. Solve the equation \$z^2 + 5z + 6 = 0 \$ for z.	A) - 2, - 2 B) - 2, - 4 C) - 2, - 3 D) - 6, 1
9	Find the square root of the complex number z = - 2 + 3i.	A) \$ sqrt(z) = \pm(sqrt(3 + sqrt(13)) / (\sqrt2) + sqrt(sqrt(13) - 3) / (\sqrt2))i \$ B) \$ sqrt(z) = \pm(sqrt(-3 - sqrt(13)) / (\sqrt2) + sqrt(sqrt(13) - 3) / (\sqrt2))i \$ C) \$ sqrt(z) = \pm(sqrt(-2 + sqrt(13)) / (\sqrt2) + sqrt(sqrt(13) + 2) / (\sqrt2))i \$ D) \$ sqrt(z) = \pm(sqrt(-1 + sqrt(13)) / (\sqrt2) + sqrt(sqrt(13) + 1) / (\sqrt2))i \$
10	Divide the complex numbers (2 - 7i) by (-3 + i).	A) \$-1/10 + 19/10 i\$ B) \$1/10 - 19/10 i\$ C) \$- 1/10 + 19/10 i\$ D) \$ 1/10 + 19/10 i\$

Problem Id

Problem

Options

Evaluate \$(1 + i)^3\$.

A) -2 + 5i

B) -1 + 2i

C) -2 + 2i

D) -2 - 2i

Solve the equation \$ z^2 + 6z + 25 = 0\$ for z.

A) z = 1 + 4i and z = 1 − 4i

B) z = −2 + 5i and z = −2 − 5i

C) z = 2 + 4i and z = 2 − 4i

D) z = −3 + 4i and z = −3 − 4i

Multiply the complex numbers (2 + 3i) and (- 1 + 2i).

A) - 4 + 3i

B) - 8 + i

C) - 6 + i

D) - 2 + 4i

Divide the complex numbers:
\$(5 + 7i) / (2 - 3i)\$.

A) \$ (-11/13) + (29/13)i \$

B) \$ (-21/11) + (25/11)i \$

C) \$ (21/11) + (25/11)i \$

D) \$ (1/13) + (29/13)i \$

Find the roots of a complex polynomial
\$z^3 + 4z^2 + 5z + 2 = 0\$.

A) z = - 1, - 1, - 2

B) z = 0, - 1, 2

C) z = 1, 1, - 2

D) z = 2, - 3, 4

Find the sum of all complex numbers z such that
\$z^3 + 2z^2 + z − 3 = 0\$.

A) - 3

B) - 2

C) - 6

D) 4

Perform operations with complex numbers. Let’s solve the following expression:
\$(3 + 2i) + (1 − 4i) times (2 + 3i)\$.

A) 15 - 3i

B) 17 - 3i

C) 11 - 5i

D) 7 - 3i

Solve a quadratic equation with complex roots.
Solve the equation \$z^2 + 5z + 6 = 0 \$ for z.

A) - 2, - 2

B) - 2, - 4

C) - 2, - 3

D) - 6, 1

Find the square root of the complex number z = - 2 + 3i.

A) \$ sqrt(z) = \pm(sqrt(3 + sqrt(13)) / (\sqrt2) + sqrt(sqrt(13) - 3) / (\sqrt2))i \$

B) \$ sqrt(z) = \pm(sqrt(-3 - sqrt(13)) / (\sqrt2) + sqrt(sqrt(13) - 3) / (\sqrt2))i \$

C) \$ sqrt(z) = \pm(sqrt(-2 + sqrt(13)) / (\sqrt2) + sqrt(sqrt(13) + 2) / (\sqrt2))i \$

D) \$ sqrt(z) = \pm(sqrt(-1 + sqrt(13)) / (\sqrt2) + sqrt(sqrt(13) + 1) / (\sqrt2))i \$

Divide the complex numbers (2 - 7i) by (-3 + i).

A) \$-1/10 + 19/10 i\$

B) \$1/10 - 19/10 i\$

C) \$- 1/10 + 19/10 i\$

D) \$ 1/10 + 19/10 i\$